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Research Papers: Offshore Technology

Second-Order Diffraction and Radiation of a Floating Body With Small Forward Speed

[+] Author and Article Information
Yan-Lin Shao

e-mail: shao.yanlin@ntnu.no

Odd M. Faltinsen

Centre for Ships and
Ocean Structures (CeSOS) and
Department of Marine Technology,
Norwegian University of Science and
Technology (NTNU),
N-7491, Trondheim, Norway

1Corresponding author.

Contributed by the Ocean Offshore and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received July 8, 2010; final manuscript received March 28, 2012; published online February 22, 2013. Assoc. Editor: Thomas Fu.

J. Offshore Mech. Arct. Eng 135(1), 011301 (Feb 22, 2013) (10 pages) Paper No: OMAE-10-1072; doi: 10.1115/1.4006929 History: Received July 08, 2010; Revised March 28, 2012

The formulation of the second-order wave-current-body problem in the inertial coordinate system involves higher-order derivatives in the body boundary condition. A new method taking advantage of the body-fixed coordinate system in the near field is presented to avoid the calculation of higher-order derivatives in the body boundary condition. The new method has an advantage over the traditional method when the body surface has a sharp corner or high curvature. The nonlinear wave diffraction and forced oscillation of floating bodies are studied up to second order in wave slope. A small forward speed is taken into account. The results of the new method are compared with that of the traditional method based on a formulation in the inertial coordinate system. When the traditional method applies, good agreement has been obtained.

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Figures

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Fig. 1

Definition of coordinate systems and the illustration of water domain, body boundary, free surfaces, control surface, bottom surface, and damping zone

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Fig. 2

An example of the meshes on SB, SF1, and SC of the inner domain

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Fig. 3

An example of meshes on the free surfaces SF1 and SF20

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Fig. 4

The amplitude of the nondimensional first-order inline force on a vertical bottom mounted circular cylinder versus kR. A is the wave amplitude. h = R, Fr = 0.1.

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Fig. 5

The amplitude of the nondimensional first-order inline force on a vertical bottom mounted circular cylinder versus kR. A is the wave amplitude. h = R, Fr =  − 0.1.

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Fig. 6

Nondimensional mean drift force on a vertical bottom mounted circular cylinder versus kR. A is the wave amplitude. h = R, Fr =  − 0.1.

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Fig. 7

The amplitude of nondimensional sum-frequency inline force on a vertical bottom mounted circular cylinder versus kR. h = R.

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Fig. 8

The nondimensional surge added mass for a vertical circular cylinder compared with the analytical results by Malenica et al. [39]. The draft is equal to the water depth h and the radius R. Fr = 0.0.

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Fig. 9

The nondimensional surge damping coefficient for a vertical circular cylinder compared with the analytical results by Malenica et al. [39]. The draft is equal to the water depth h and the radius R. Fr = 0.0.

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Fig. 10

The nondimensional surge added mass for a vertical circular cylinder compared with the analytical results by Malenica et al. [39]. The draft is equal to the water depth h and the radius R. Fr =  − 0.05.

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Fig. 11

The nondimensional surge damping coefficient for a vertical circular cylinder compared with the analytical results by Malenica et al. [39]. The draft is equal to the water depth h and the radius R. Fr =  − 0.05.

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Fig. 12

The mean drift force and the amplitude of the sum-frequency force on a vertical circular cylinder versus kR. The draft is equal to the water depth h and the radius R. Fr = 0.05. The surge amplitude is 0.05R.

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Fig. 13

Sketch of a section of the axisymmetric body in the oxz plane

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Fig. 14

Time history of the first-order wave force in the x direction on the axisymmetric body defined in Fig. 13 under forced pitching about COG. Fr = U/gR = 0.05, kR = 1.2.

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Fig. 15

Time history of the first-order wave force in the z direction on the axisymmetric body defined in Fig. 13 under forced pitching about COG. Fr = U/gR = 0.05, kR = 1.2.

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Fig. 16

Time history of the first-order pitch moment about an axis through COG for the axisymmetric body defined in Fig. 13 under forced pitching about COG. Fr = U/gR = 0.05, kR = 1.2.

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Fig. 17

Time history of the second-order wave force in the z direction on the axisymmetric body defined in Fig. 13 under forced pitching about COG. Fr = U/gR = 0.05, kR = 1.2.

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Fig. 18

Amplitude of the sum-frequency force in the z direction versus kR for an axisymmetric body defined in Fig. 13 under forced pitch motion about COG. Fr = 0.05.

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